On the response of the Einstein Telescope to Doppler anisotropies

Abstract

We study the response function of the Einstein Telescope to kinematic Doppler anisotropies, which represent one of the guaranteed properties of the stochastic gravitational wave background. If the frequency dependence of the stochastic background changes slope within the detector frequency band, the Doppler anisotropic contribution to the signal can not be factorized in a part depending on frequency, and a part depending on direction. For the first time, we study the detector response function to Doppler anisotropies without making any factorizable Ansatz. Moreover, we do not assume that kinematic effects are small, and we derive general formulas valid for any relative velocity among frames. We apply our findings to three well-motivated examples of background profiles: power-law, broken power-law, and models with a resonance motivated by primordial black hole scenarios. We derive the signal-to-noise ratio associated with an optimal estimator for the detection of non-factorizable kinematic anisotropies, and we study it for representative examples.

v1: 19+9 pages, 11 figures; v2: 21+9 pages, 10 figures, improved version, published in Phys. Rev. D

References in corpus (16)

• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves
• Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak
• Probing Anisotropies of the Stochastic Gravitational Wave Background with LISA
• Constraining the Solution to the Last Parsec Problem with Pulsar Timing
• Testing the Early Universe with Anisotropies of the Gravitational Wave Background
• Enhancing gravitational wave anisotropies with peaked scalar sources
• Intensity and anisotropies of the stochastic Gravitational Wave background from merging compact binaries in galaxies
• Probing anisotropies of gravitational-wave backgrounds with a space-based interferometer III: Reconstruction of a high-frequency skymap
• Doppler boosting the stochastic gravitational wave background
• The Dipole of the Astrophysical Gravitational-Wave Background
• Disentangling Multiple Stochastic Gravitational Wave Background Sources in PTA Datasets
• Targeted search for the kinematic dipole of the gravitational-wave background
• Primordial Stochastic Gravitational Wave Background Anisotropies: in-in Formalization and Applications
• The rise of the primordial tensor spectrum from an early scalar-tensor epoch

Cited by in corpus (6)

• The Science of the Einstein Telescope
• Measuring kinematic anisotropies with pulsar timing arrays
• Primordial Gravitational Waves as Probe of Dark Matter in Interferometer Missions: Fisher Forecast and MCMC
• Untargeted Bayesian search of anisotropic gravitational-wave backgrounds through the analytical marginalization of the posterior
• Astrometry meets Pulsar Timing Arrays: Synergies for Gravitational Wave Detection
• Gravitational Wave Signatures of Primordial Black Hole Reheating in Upcoming Interferometry Missions